Question: Which of the following numbers is a multiple of 11? ${59,64,76,79,88}$
The multiples of $11$ are $11$ $22$ $33$ $44$ ..... In general, any number that leaves no remainder when divided by $11$ is considered a multiple of $11$ We can start by dividing each of our answer choices by $11$ $59 \div 11 = 5\text{ R }4$ $64 \div 11 = 5\text{ R }9$ $76 \div 11 = 6\text{ R }10$ $79 \div 11 = 7\text{ R }2$ $88 \div 11 = 8$ The only answer choice that leaves no remainder after the division is $88$ $ 8$ $11$ $88$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $88$ $88 = 2\times2\times2\times11 11 = 11$ Therefore the only multiple of $11$ out of our choices is $88$. We can say that $88$ is divisible by $11$.